Typology

"Inverse distance" weighting, "radial basis" functions, "splines", "ordinary kriging", "natural neighbor", "polynomial regression" methods, "universal kriging", etc. These are just some interpolation methods found in commercial software. The diversity of methods and their parameterizations can be confusing. Therefore, we will first try to classify the methods into schemes. In the following table, different approaches can be seen:

Local vs. global interpolation

Global methods are applied to ALL data in the study area; local methods on the other hand, are only applied to spatially defined subsets. Global interpolation is therefore not suited for the determination of exact values but to assess global spatial structures.

As examples, you can see a linear trend surface which was determined by regression from Swiss rainfall data and shows a trend toward increased precipitation totals from SE to NW, and a local interpolation using a radial basis interpolation:

Exact vs. approximate interpolation

Exact interpolation means: the estimated surface passes through all points whose values are known. In approximate interpolation, the estimates of known points can vary from known values. The latter method can be usefully applied when the known data is already somewhat fuzzy.

Gradual vs. abrupt interpolation

This distinction mainly refers to the resulting estimation surface. Were there breaklines (naturally abrupt changes in values such as in cliffs or lakefronts) included in the interpolation or not?

Deterministic vs. stochastic interpolation

Techniques of deterministic interpolation are based on exactly predetermined (= deterministic) spatial contexts; in stochastic approaches on the other hand, random elements have an impact as well. Deterministic methods show clear disadvantages in interpolating natural spatial phenomena, since a given degree of uncertainty always exists.